The anisotropy of a granular material's structure will influence its response to applied loads and deformations. Anisotropy can be either inherent (e.g. due to depositional process) or induced as a consequence of the applied stresses or strains. Discrete element simulations allow the interactions between individual particles to be explicitly simulated and the fabric can be quantified using a fabric tensor. The eigenvalues of this fabric tensor then give a measure of the anisotropy of the fabric. The coordination number is a particle scale scalar measure of the packing density of the material. The current study examines the evolution of the fabric of a granular material subject to cyclic loading, using two-dimensional discrete element method (DEM) simulations. Isotropic consolidation modifies and reduces the inherent anisotropy, but anisotropic consolidation can accentuate anisotropy. The

The present study aims to elucidate the anisotropic characteristics in material responses for crystallographic nickel substrates with (001), (011) and (111) surface orientations during nanoindentation. Molecular dynamic simulation is applied to compensate for the experimental limitation of nanoindentation, particularly for pure nickel substrates. Defect nucleation and evolution in Ni single crystal of these three crystal orientations was examined. Hardness and Young's modulus are also extracted in different orientations. The Young's modulus of (111) crystallographic orientation is the largest, while that of (001) surface is the smallest. The sensitivity of the yield point for face centred cubic crystals depends on the crystallographic orientation. The (001) crystallographic orientation reaches the yield point first, while the (111) crystallographic orientation is the most difficult in which to achieve yield. Using a visualisation method of centrosymmetry parameter, the homogeneous nucleation and early evolution of dislocations were investigated, deepening understanding of incipient plasticity at the atomic scale. The present results suggest that defect nucleation and evolution are the root of curve jitter. The indentation depth of the elastic–plastic transition point varies in the different crystallographic orientation models, and appears latest in the (111) model. The strain energy of the substrate exerted by the tip is stored by the formation of homogeneous nucleation and is dissipated by the dislocation slide in the {111} glide plane. The three nickel substrates with different crystallographic orientations exhibit different forms of dislocation propagation.

Based on the Blot's theory about two-phase saturated medium, according to the character of 6 function, the Green function on two-phase saturated medium by the point source under concentrated force can be derived. By the Betti's theorem for the two-phase saturated medium field, the source vector and static displacement field by elastic dislocation on the two-phase saturated medium were comprehensively discussed.

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